Internal
problem
ID
[10893]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
9,
system
of
higher
order
odes
Problem
number
:
1921
Date
solved
:
Friday, October 11, 2024 at 12:20:26 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \frac {d}{d t}x \left (t \right )&=-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )\\ \frac {d}{d t}y \left (t \right )&=\left \{\begin {array}{cc} x \left (t \right )^{2}+y \left (t \right )^{2} & 2 x \left (t \right )\le x \left (t \right )^{2}+y \left (t \right )^{2} \\ \left (\frac {x \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{2 x \left (t \right )}\right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) & \operatorname {otherwise} \end {array}\right . \end{align*}
10.9.2 Maple dsolve solution
Solving time : 74.384 (sec)
Leaf size : maple_leaf_size
\[ \text {No solution found} \]
10.9.3 Mathematica DSolve solution
Solving time : 0.0 (sec)
Leaf size : 0
DSolve[{{D[x[t],t]==-y[t]*(x[t]^2+y[t]^2),D[y[t],t]==Piecewise[{{(x[t]^2+y[t]^2),(x[t]^2+y[t]^2)>=2*x[t]},{(x[t]/2-y[t]^2/(2*x[t]))*(x[t]^2+y[t]^2),True}}]},{}},
{x[t],y[t]},t,IncludeSingularSolutions->True]
Not solved